This is more of an analog circuit. Here's some links to analog computers, specific and general purpose. The computing in empty space concept is particularly interesting. One of these is very practical with a huge speedup on numerical computation on the cheap.

Another little-known use of analog is obfuscating trade secrets in ASIC's. One hardware engineer that used to post on Schneier's blog told us how most engineers and tools did digital with little understanding of analog or especially combinations of the two ("mixed signal"). So, he would put parts of the critical algorithms in analog with odd tie-ins to the digital side. Integrating their I.P. with digital tools was still easy but ripping it off required analog or mixed-signal experts spending a lot of time. A trick worth remembering.

The Vintage Computing Festival in Berlin which ran this weekend had a room dedicated to analog computers, most of them still working, with instructors, demo programs and one could even play around with them. A 'program' is basically a set of wires that connect blocks like oscillators, integrators, filters, etc... you started with some mathematical formula you wanted to solve (mostly some integration problem), translated this into a 'block diagram', built this with wires, and then you could fiddle around at the dials and knobs and see how the result changed on an oscilloscope. I was told that this was mainly used to simulate how complex real-world industrial systems like coal energy plant components would behave under extreme conditions. At least that's how I understood it all :)

Also interesting: the Soviets built analog water computers starting in the late 1920s which could solve specific problems so fast that digital computers needed 50 years to do the same thing in comparable time: http://www.digitaljournal.com/article/338106

Of course they had noise problems. They were using a solderless breadboard. Analog computers require shielding, good ground planes, and bypass caps on power at each IC.

I once had two 555 timers, set up as oscillators, on a solderless breadboard, and they'd phase-lock just from inductive coupling if they were near the same frequency. Without bypass caps at each IC, they'd phase-lock even when the frequencies weren't close, at some ratio like 7:6. When the big power transistor in a 555 switches, it introduces a transient, which gets into the input signals. Fun to watch on a scope.

While you can build analog differentiators, they're so noise-sensitive that they're almost useless. Combined differentiators and low-pass filters can work, but a pure differentiator tries to track the slope of every tiny noise event. Analog computing is usually all integrators, summers, and multipliers, as they did here.